Method and apparatus for multilayer shear band reinforcement

ABSTRACT

A method is provided for reinforcement of a multiple layer shear band as may be used in a non-pneumatic tire. More particularly, a method of improving the performance characteristics (such as e.g., increasing the bending stiffness) of a shear band without increasing its thickness or to reducing the thickness of a shear band while maintaining its performance characteristics and to shear bands constructed according to such method is provided as well as shear bands constructed according to such method.

PRIORITY CLAIM

The present application is a divisional application that claims priorityto U.S. application Ser. No. 13/497,618, filed on Mar. 22, 2012, whichis a U.S. national stage application for PCT/US2009/060746, filed Oct.15, 2009.

FIELD OF THE INVENTION

The present invention relates to reinforcement of a multiple layer shearband as may be used in a non-pneumatic tire and to a method of designingsuch a shear band. More particularly, the present invention relates to amethod of improving the performance characteristics (such as e.g.,increasing the bending stiffness) of a shear band without increasing itsthickness or to reducing the thickness of a shear band while maintainingits performance characteristics and to shear bands constructed accordingto such method.

BACKGROUND OF THE INVENTION

The details and benefits of non-pneumatic tire constructions aredescribed e.g., in U.S. Pat. Nos. 6,769,465; 6,994,134; 7,013,939; and7,201,194. Certain non-pneumatic tire constructions proposeincorporating a shear band, embodiments of which have also beendescribed in e.g., U.S. Pat. No. 7,201,194, which is incorporated hereinby reference. Such non-pneumatic tires provide advantages in tireperformance without relying upon a gas inflation pressure for support ofthe loads applied to the tire.

An example of a tire 100 having a ring-shaped shear band 110 is shown inFIG. 1. Tire 100 also includes a plurality of tension transmittingelements, illustrated as web spokes 150, extending transversely acrossand inward from shear band 110. A mounting band 160 is disposed at theradially inner end of the web spokes. The mounting band 160 anchors thetire 100 to a hub 10. A tread portion 105 is formed at the outerperiphery of the shear band 110 and may include e.g., grooves or ribsthereon.

Referring to FIG. 2, which shows the tire 100 in section view in themeridian plane (but without tread portion 105), the reinforced shearband 110 comprises a shear layer 120, an innermost reinforcement layer130 adhered to the radially innermost extent of the shear layer 120, andan outermost reinforcement layer 140 adhered to the radially outermostextent of the shear layer 120. The reinforcement layers 130 and 140 havea tensile stiffness that is greater than the shear stiffness of theshear layer 120 so that the shear band 110 undergoes shear deformationunder vertical load.

More specifically, as set forth in U.S. Pat. No. 7,201,194, when theratio of the elastic modulus of the reinforcement layer to the shearmodulus of the shear layer (E′_(membrane)/G), as expressed in U.S. Pat.No. 7,201,194, is relatively low, deformation of shear band 110 underload approximates that of a homogenous band and produces a non-uniformground contact pressure. Alternatively, when this ratio is sufficientlyhigh, deformation of the shear band 110 under load is essentially byshear deformation of the shear layer with little longitudinal extensionor compression of the reinforcement layers 130 and 140. As indicated inFIG. 1, a load L placed on the tire axis of rotation X is transmitted bytension in the web spokes 150 to the annular band 110. The annular shearband 110 acts in a manner similar to an arch and providescircumferential compression stiffness and a longitudinal bendingstiffness in the tire equatorial plane sufficiently high to act as aload-supporting member. Under load, shear band 110 deforms in contactarea C with the ground surface through a mechanism including sheardeformation of the shear band 110. The ability to deform with shearprovides a compliant ground contact area C that acts similar to that ofa pneumatic tire, with similar advantageous results.

The shear layer 120 may be constructed e.g., from a layer of materialhaving a shear modulus of about 3 MPa to about 20 MPa. Materialsbelieved to be suitable for use in the shear layer 120 include naturaland synthetic rubbers, polyurethanes, foamed rubbers and polyurethanes,segmented copolyesters, and block co-polymers of nylon. The first 130and second 140 reinforcement layers comprise essentially inextensiblecord reinforcements embedded in an elastomeric coating. For a tireconstructed of elastomeric materials, reinforcement layers 130 and 140are adhered to the shear layer 120 by the cured elastomeric materials.

As stated above, a shear band such as band 110 provides a longitudinalbending stiffness during operation of the tire 100. For certainapplications, it is desirable to maintain the overall thickness—alongthe radial direction R—of shear band 110 while simultaneously increasingits bending stiffness. For example, a designer may seek to maintain theoverall diameter of non-pneumatic tire 100 and the shear beam thicknesswhile increasing the bending stiffness of the shear band 110 in order tochange the performance characteristics of tire 100. Conversely, forcertain other applications, it is desirable to decrease the thickness ofshear band 110 while maintaining the bending stiffness of tire 100 andthus reduce mass.

Accordingly, a method for the design of such shear bands and shear bandsconstructed from such method would be particularly useful. Moreparticularly, a method that allows the designer of a non-pneumatic tireto improve certain mechanical properties of a reference shear band suchas e.g., bending stiffness while maintaining the overall dimensions ofthe non-pneumatic tire would be particularly useful. A method that alsoallows a designer to decrease the radial thickness of a shear band whilemaintaining or improving upon certain mechanical properties would alsobe useful. These and other advantageous aspects of the present inventionwill be apparent from the description that follows.

SUMMARY OF THE INVENTION

Objects and advantages of the invention will be set forth in part in thefollowing description, or may be obvious from the description, or may belearned through practice of the invention.

In one exemplary aspect of the present invention, a method is providedfor modifying a shear band having a thickness of H_(REF) and a totalnumber of reinforcement layers of N_(REF). The method includesdetermining the vertical stiffness and (G_(eff)*A)_(REF) using athickness of H_(REF) for the shear band and a total of N_(REF)reinforcement layers for the shear band; selecting a target valueH_(TARGET) for the thickness of the shear band; increasing by 1 thetotal number of reinforcement layers in the shear band; calculating(G_(eff)*A)_(CALC) using a thickness of H_(TARGET) for the shear bandand using the number of reinforcement layers for the shear band providedby the increasing step; comparing (G_(eff)*A)_(CALC) from thecalculating step with (G_(eff)*A)_(REF) from the determining step and,if (G_(eff)*A)_(CALC) is less than (G_(eff)*A)_(REF), then repeating theincreasing step and the calculating step until (G_(eff)*A)_(CALC) isgreater than or about equal to (G_(eff)*A)_(REF) and the total number ofreinforcement layers becomes N_(TOTAL); and computing the verticalstiffness using a thickness of H_(TARGET) for the shear band and thenumber of reinforcement layers N_(TOTAL) for the shear band provided bythe comparing step. If the vertical stiffness from the computing step isless than the vertical stiffness from the determining step, then themethod includes moving at least one of the reinforcement layers betweenan outermost reinforcement layer and an innermost reinforcement layer toa new position in the shear band that is closer to either the outermostreinforcement layer or the innermost reinforcement layer, and repeatingthe computing and referring steps until the vertical stiffness from thecomputing step is greater than or about equal to the vertical stiffnessfrom the determining step.

In another exemplary embodiment of the present invention, a method isprovided for modifying a shear band having a radially innermostreinforcement layer and a radially outermost reinforcement layer. Themethod includes the steps of increasing or maintaining the verticalstiffness of a non-pneumatic tire incorporating the shear band by addingat least one additional reinforcement layer that is positioned between,but spaced apart from, the radially outermost reinforcement layer andthe radially innermost reinforcement layer; and decreasing the value ofμ_(p/p) for the shear band.

Variations to this exemplary method of the present invention are furtherdescribed in the detailed description the follows. The present inventionalso includes a shear band constructed according to this exemplarymethod and to a non-pneumatic tire incorporating such a shear band.

For example, in one exemplary embodiment, the present invention includesa shear band having a shear layer, an inner reinforcement layerpositioned along one side of said shear layer, and an outerreinforcement layer positioned along the other side of said shear layersuch that said shear layer is positioned between said inner and outerreinforcement layers. At least two or more additional reinforcementlayers are positioned between and spaced apart from each other and fromsaid outer and inner reinforcement layers such that the shear band has atotal of N reinforcement layers and N≧4.

These and other features, aspects and advantages of the presentinvention will become better understood with reference to the followingdescription and appended claims. The accompanying drawings, which areincorporated in and constitute a part of this specification, illustrateembodiments of the invention and, together with the description, serveto explain the principles of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure of the present invention, including thebest mode thereof, directed to one of ordinary skill in the art, is setforth in the specification, which makes reference to the appendedfigures, in which:

FIG. 1 is a schematic view in the equatorial plane of a non-pneumatictire under load.

FIG. 2 is a schematic view in the meridian plane of a loaded shear bandas used in the non-pneumatic tire of FIG. 1. The tread portion of thenon-pneumatic tire is not shown in FIG. 2.

FIG. 3 is a schematic view in the meridian plane of an exemplaryembodiment of a shear band of the present invention. The shear band hasfive reinforcement layers i.e., three reinforcement layers are addedbetween the innermost and outermost reinforcement layers.

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates to reinforcement of a multiple layer shearband as may be used in a non-pneumatic tire and to a method of designingsuch a shear band. More particularly, the present invention relates to amethod of improving the performance characteristics (such as e.g.,increasing the bending stiffness) of a shear band without increasing itsthickness or to reducing the thickness of a shear band while maintainingits performance characteristics and to shear bands constructed accordingto such method. For purposes of describing the invention, reference nowwill be made in detail to embodiments and methods of the invention, oneor more examples of which are illustrated in the drawings. Each exampleis provided by way of explanation of the invention, not limitation ofthe invention. In fact, it will be apparent to those skilled in the artthat various modifications and variations can be made in the presentinvention without departing from the scope or spirit of the invention.For instance, features illustrated or described as part of oneembodiment, can be used with another embodiment to yield a still furtherembodiment. Thus, it is intended that the present invention covers suchmodifications and variations as come within the scope of the appendedclaims and their equivalents.

The following terms are defined as follows for this description:

“Equatorial Plane” means a plane that passes perpendicular to the tireaxis of rotation and bisects the tire structure.

“Meridian Plane” means a plane that passes through and includes the axisof rotation of the tire.

“Vertical stiffness” is a mathematical relationship between deflectionand load for a tire. As described in U.S. Pat. No. 7,201,194, when anon-pneumatic tire containing a shear band is placed under a load L, itdeflects a certain amount f and the portion in ground contact conformsto the ground surface to form a ground contact area C. Because the shearband provides a resilient tire, vertical deflection f is proportional tothe load L, from which the vertical stiffness of the resilient tire maybe derived. There are numerous ways that one of ordinary skill in theart can provide or define a mathematical relationship between deflectionand load for a tire. Two such examples, secant vertical stiffness andtangent vertical stiffness, are defined below.

“Secant vertical stiffness” is an example of a mathematical relationshipdefining vertical stiffness as the quotient of L/f or the load L placedon the non-pneumatic tire divided by the deflection f of the tire asdiscussed for vertical stiffness above. For a given tire, a plot can becreated by measuring deflection for multiple loads L.

“Tangent vertical stiffness” is another example of a mathematicalrelationship defining vertical stiffness as the slope of a line tangentto a curve created by plotting load L as a function of deflection f fora given non-pneumatic tire containing a shear band at a target load ordeflection.

“Contact Pressure” means the average contact pressure for contact area Ccreated by a non-pneumatic tire loaded against the ground or othersupporting surface and can be calculated as the quotient of load Ldivided by the contact area C.

“μ_(p/p)” is a measurement of the peak-to-peak radial displacement of ashear band under load as incorporated into a non-pneumatic tire. Asdescribed in U.S. Pat. No. 7,013,939, which is incorporated herein byreference, μ_(p/p) is a measurement of the buckling or radialdisplacement that a band can exhibit (which can result in uneven rollingof the tire containing such shear band) when compression forces exceedthe ability of the band to shorten. As will be used herein, the peak topeak radial displacement, μ_(p/p), can be calculated as follows for ashear band comprising multiple reinforcement layers connected by spokesto a hub such as shown in FIGS. 1 and 2:

$\begin{matrix}{\mu_{p/p} \cong {1.5\left( \frac{1 - v^{2}}{E_{membrane}I_{m}} \right){T\left( \frac{r_{0}}{n} \right)}^{3}}} & (1)\end{matrix}$

where

-   -   μ_(p/p) is the peak to peak radial displacement (mm);    -   ν is the Poisson's ratio of the shear band;    -   E_(membrane) is the modulus of elasticity of a reinforcement        layer (N/mm²);    -   I_(m) is the area moment of inertia of the reinforcement layers        (mm⁴);    -   T is the spoke tension (N);    -   r₀ is the nominal radius of the shear band (mm); and    -   n is the number of spokes.

E_(membrane) is the homogenized circumferential modulus of elasticity ofa reinforcement layer expressed in units of N/mm². E_(membrane) for thereinforcement layer may be determined experimentally by ASTM Test MethodD 3039, “Standard Test Method for Tensile Properties of Polymer MatrixComposite Materials.” For the specific example of a reinforcement layerhaving cords or cable reinforcements at zero degrees (i.e. perpendicularto the equatorial plane) E_(membrane) may be calculated from thefollowing equation:E _(membrane) =E _(matrix) *V _(fm) +E _(cable) *V _(fc)  (2)

where,

-   -   t is the thickness of the reinforcement layer (mm)    -   E_(matrix) is the modulus of the matrix or the material making        up the non-cable portion of the reinforcement layer (N/mm²)    -   V_(fm) is the matrix volume fraction    -   E_(cable) is the cable tensile modulus (N/mm²)    -   V_(fc) is the cable volume fraction

For purposes of describing the present invention, consider non-pneumatictire 100 of FIGS. 1 and 2 as a reference, having a shear band 110thickness H_(REF) of 18 mm in thickness, a tread layer 105 of 3.5 mm inthickness, a total tire thickness of 21.5 mm, and a total number ofreinforcement layers N_(REF) of two. This reference tire 100 also has anoutside diameter D_(o) of 630 mm and has 50 spokes with a nominalthickness of 3.8 mm. Also, reinforcement layers 130 and 140 each have anominal E_(membrane) of 2000 daN/mm² and a thickness of 1 mm. Note thatfor the sake of clarity in the quantitative values described herebelow,the units of Newtons have been replaced by decaNewtons wherein 1 daN isequal to 10 N.

The performance of non-pneumatic tire 100 as a reference can beevaluated by considering four performance characteristics: TangentVertical Stiffness, Secant Vertical Stiffness, Contact Pressure, andμ_(p/p). Using finite element analysis of a model of non-pneumatic tire100, the values for these performance characteristics were determined ata vertical load of 400 daN and are set forth in Table 1.

TABLE 1 Vertical Vertical Stiffness Stiffness Contact (Tangent) (Secant)Pressure μ_(p/p) 33.6 daN/mm 41.0 daN/mm 2.3 bar .056 mm

For purposes of describing the present invention, assume these referencevalues provide acceptable performance for the intended application ofshear band 110. However, for this intended application, assume also thatfor tire 100 a tread thickness of 6.5 mm is desired instead of the 3.5mm thick tread portion 105 specified above—i.e., a assume a 3 mmincrease in thickness for tread portion 105 is needed while all otherfeatures of tire 100 such as e.g., hub 10, spokes 150, tire size, andthe materials of construction are acceptable without changes. Therefore,in order to maintain the outside diameter D_(o) of tire 100 at 630 mm,shear band 110 might be reduced by 3 mm to a target shear band thicknessH_(TARGET) of 15 mm in order to accommodate the desired increase inthickness of tread portion 105. Again, using finite element analysis ofa model of tire 100, the performance characteristics for tire 100 with areduction in thickness of 3 mm for shear band 110 were determined andare set forth in Table 2.

TABLE 2 Vertical Vertical Stiffness Stiffness Contact (Tangent) (Secant)Pressure μ_(p/p) 30.0 daN/mm 36.6 daN/mm 2.0 bar .065 mm

Unfortunately, as demonstrated by the results in Table 2, reducing thethickness of the shear band 110 adversely impacts the performance ofnon-pneumatic tire 100 and does not meet the four acceptable (i.e.,target) performance characteristics for the reference tire 100 that areset forth in Table 1 (i.e., the performance characteristics of tire 100before reducing the thickness of the shear band 110). More specifically,reducing the thickness of shear band 110 has the adverse impact ofdecreasing the band's stiffness and increasing the potential for peak topeak radial displacement μ_(p/p) during operation. Therefore, in orderto reach the desired design targets set forth in Table 1, certainmodifications must be undertaken for shear band 110 if its thickness isto be reduced. Similarly, modifications would also be needed if thedesigner decided to maintain the reference thickness for shear band 110,H_(REF), while increasing its vertical stiffness.

Therefore, in one exemplary aspect, the present invention provides amethod for adding reinforcement to a shear band. However, the presentinvention does not propose adding reinforcement by increasing theexisting reinforcement layers 130 and 140 or adding reinforcementcontiguous thereto. Instead, using the methods disclosed herein, theinventors have made the unexpected discovery that by addingreinforcement layers into the shear layer 120 at radial locations thatare between, but spaced apart from, the existing reinforcement layers130 and 140, not only can the desired vertical stiffness characteristicsbe achieved but an unexpected improvement (i.e., reduction) in radialdisplacement of the shear band, as measured by μ_(p/p) can also beaccomplished.

In addition, flexibility is provided in that the added reinforcementlayers can be uniformly spaced between the existing reinforcement layers130 and 140 or, if desired, such additional layers can be spaced in amanner that is not uniform. Flexibility is also provided in that thepresent invention may be used to reduce H_(REF) (the thickness of thereference shear band 110) while maintaining or improving upon certainperformance characteristics such as e.g., its bending stiffness.Alternatively, the present invention may be used to improve itsperformance characteristics (e.g., increasing vertical stiffness)without changing H_(REF). Accordingly, using the reference values ofTable 1 as the target values, an exemplary application of the method ofthe present invention in order to reduce the thickness of referenceshear band 110 by 3 mm now follows.

The inventors have determined that the four performance characteristicsset forth in Table 1 for the reference shear band 110 are controlled bythree products set forth in equations (3), (4), and (5) below, which canbe thought of as three structural section properties of shear band 110.Before addressing these equations, it should be noted that the followingequations (3) through (8) are based on the assumption that thereinforcement layers are uniform relative to each other. However, aswill be understood by one of skill in the art using the teachingsdisclosed herein, the method described herein may also be applied to ashear band having reinforcement layers that are not uniform. Forexample, reinforcement layers of different thicknesses may also beapplied using the present invention. Accordingly, for uniformreinforcement layers, the three products—i.e., three structural sectionproperties—can be expressed as follows:G _(eff) *A  (3)E _(membrane) *I _(m)  (4)E _(membrane) *A _(m)  (5)

where

-   -   G_(eff) is the effective shear modulus of shear band 110        including the reinforcement layers 130, 140;    -   A is the total cross sectional area of the shear band 110 (not        including the tread layer);    -   E_(membrane) is the circumferential modulus of the reinforcement        layers 130 and 140;    -   I_(m) is the contribution to the area moment of inertia of the        reinforcement layers; and    -   A_(m) is the total cross-sectional area of the reinforcement        layers.

G_(eff), the effective shear modulus of shear band 110, is calculated asfollows:

$\begin{matrix}{G_{eff} = \frac{G_{m}G_{sl}H}{{G_{sl}{Nt}} + {G_{m}\left( {H - {Nt}} \right)}}} & (6)\end{matrix}$

where

-   -   G_(m) is the shear modulus of the reinforcement layers;    -   G_(sl) is the shear modulus of the elastomer used for the shear        layer;    -   H is the total thickness of the shear band including        reinforcement the layers;    -   N is the total number of reinforcement layers; and    -   t is the thickness of the reinforcement layers;

The area moment of the inertia, I_(m), is calculated by one of thefollowing two equations depending upon whether an even or odd number ofreinforcement layers are used in shear band 110. For an even number ofreinforcement layers, the area moment of inertia I_(m) will be expressedas I_(Neven), and the following equation provides for the calculation ofI_(Neven):

$\begin{matrix}{I_{Neven} = {{NI}_{0} + {2{{tw}\left\lbrack {h_{Beven}^{2} + {\sum\limits_{i = 1}^{\frac{N}{2} - 1}\left( {h_{Beven} + h_{N}} \right)^{2}}} \right\rbrack}}}} & (7)\end{matrix}$

where

-   -   w is the width of a reinforcement layer;    -   t is the thickness of a reinforcement layer along radial        direction R;    -   h_(N) is the distance, along the radial direction R, from the        center of one reinforcement layer to the center of the next        reinforcement layer;    -   I₀ is the area moment of inertia of an individual reinforcement        layer about its own axial centerline;    -   h_(Beven) is calculated as

${h_{Beven} = \frac{\left( {H - t} \right) - {\left( {N - 2} \right)h_{N}}}{2}};$h_(N) = (h_(ma x) − h_(m i n))k + h_(m i n);${h_{{ma}\; x} = \frac{H - t}{N - 1}};$${h_{m\; i\; n} = \frac{3t}{2}},$and;

-   -   k is a spacing bias parameter, where a value of 1 is used for        relatively equal spacing between the reinforcement layers        whereas a value of 0 gives a minimum spacing of the outer        reinforcement layers.

For an odd number of reinforcement layers as shown in FIG. 3, the areamoment of inertia I_(m) will be expressed as I_(Nodd), and the followingequation provides for the calculation of I_(Nodd):

$\begin{matrix}{{I_{Nodd} = {{NI}_{0} + {2{{tw}\left\lbrack {h_{Bodd}^{2} + {\sum\limits_{i = 1}^{\frac{N - 1}{2} - 1}\left( {h_{Bodd} + h_{N}} \right)^{2}}} \right\rbrack}}}}{where}{{h_{Bodd} = \frac{\left( {H - t} \right) - {\left( {N - 3} \right)h_{N}}}{2}};{and}}{I_{0} = {\left( {1/12} \right)*W*{t^{3}.}}}} & (8)\end{matrix}$

Calculated as shown above, the three structural section propertiesG_(eff)*A, E_(membrane)*I_(m), and E_(membrane)*A_(m) can be used toreconstruct shear band 110 as needed while still meeting (or improvingupon) the target performance characteristics of reference tire 100 setforth in Table 1. For the example introduced above, it is desired toreduce the overall thickness H of the reference shear band 110 by 3 mmwhile still meeting or improving upon the performance characteristics ofTable 1. However, other changes to shear band 110 can also beaccomplished using the methods of the present invention as well. Forexample, the original value of the shear band 110 thickness (H_(REF))could be targeted for reduction by as much as 50 percent. In fact, anyvalue for the desired thickness shear band 110 may be targeted(H_(TARGET)), provided such value is at least four times the thicknessof a reinforcement layer (t). Alternatively, the methods of the presentinvention also allow for the original value of the shear band thicknessH_(REF) to remain constant while the values for Secant VerticalStiffness and Tangent Vertical Stiffness are increased or μ_(p/p) isdecreased. Regardless, as part of an exemplary method of the presentinvention, a value for H_(TARGET) is specified for the new constructionof shear band 110, where H_(TARGET) may be the same or smaller thanH_(REF).

Using the selected target value for thickness H_(TARGET), the structuralsection property G_(eff)*A is then calculated for a shear band having atleast one additional reinforcement layer as compared to the referenceshear band 110. For example, reference shear band 110 is shown as havingtwo reinforcement layers 130 and 140, or an N_(REF) value equal to 2.Accordingly, a new G_(eff)*A is calculated, (G_(eff)*A)_(CALC), for theshear band now having three reinforcement layers and a thickness ofH_(TARGET), but otherwise constructed in a manner similar to shear band110 (It should be noted that, as used herein, N can be any positiveinteger greater than 1. For example, the reference shear band for whichmodification is desired could already have three reinforcement layers,an N_(REF) value equal to 3).

The new (G_(eff)*A)_(CALC) as determined using three reinforcementlayers (N=3) is then compared to (G_(eff)*A)_(REF) for the referenceshear band 110. If the newly calculated (G_(eff)*A)_(CALC) is less thanthe reference value of (G_(eff)*A)_(REF) for reference shear band 110,then the number of reinforcement layers is again increased by one (N=4)and the value for (G_(eff)*A)_(CALC) is again recalculated. This processis repeated until the new value for (G_(eff)*A)_(CALC) is greater thanor about equal to the original value of (G_(eff)*A)_(REF) for thereference shear band 110 with only two reinforcement layers 130 and 140,or N_(REF)=2. As used herein, N_(TOTAL) represents the total number ofreinforcement layers when (G_(eff)*A)_(CALC) becomes greater than orabout equal to the original value of (G_(eff)*A)_(REF).

The process of increasing the number of reinforcement layers N until thenew value (G_(eff)*A)_(CALC) is more than the reference value for(G_(eff)*A)_(REF) can be repeated until the following limit is reached:(H _(TARGET) −Nt)/(N−1)≦t/2  (9)This limit ensures that there will be a distance of at least one-halfthe thickness of a single reinforcement layer between adjacentreinforcement layers (assuming equal spacing). For equally spacedreinforcement layers, it should be noted that an addition that createsan odd number of reinforcement layers will proportionally increaseG_(eff)*A and E_(membrane)*A_(m) but will have a much more limitedimpact on E_(membrane)*I_(m) because at least one reinforcement layerwill be positioned about the middle or “neutral fiber” of the shearlayer. If the limit of equation (9) is reached before the value of(G_(eff)*A)_(CALC) becomes greater than the reference value(G_(eff)*A)_(REF), then the value for thickness H_(TARGET) must beincreased and the process repeated—i.e., starting again with a total ofN_(REF)+1 reinforcement layers—until the new (G_(eff)*A)_(CALC) is at orabove the reference value of (G_(eff)*A)_(REF).

Upon adding an additional reinforcement layer that provides a(G_(eff)*A)_(CALC) close to or above the reference value of(G_(eff)*A)_(REF), the values for E_(membrane)*A_(m) areE_(membrane)*I_(m) at the new number of reinforcement layers can also becalculated. The new value for E_(membrane)*A_(m) will always exceed thereference values of E_(membrane)*A_(m) because this structural sectionproperty is directly affected by the number of reinforcement layers andbecause at least one reinforcement layer has been added to the originalshear band 110 at this point in the process. However, the computed valuefor E_(membrane)*I_(m) may not meet or exceed the reference value forE_(membrane)*I_(m).

Using H_(TARGET) and N_(TOTAL) (the number of reinforcement layers atwhich (G_(eff)*A)_(CALC) exceeded the reference (G_(eff)*A)_(REF)), thevalues of the four performance characteristics—i.e., the TangentVertical Stiffness, Secant Vertical Stiffness, Contact Pressure, andμ_(p/p)—are determined using e.g., finite element analysis and a modelof the tire with the shear band now having N_(TOTAL) reinforcementlayers. The new values for the Tangent Vertical Stiffness, SecantVertical Stiffness, Contact Pressure and μ_(p/p) are then compared tothe original reference values (e.g., the values in Table 1). If the newvalues meet or exceed the original reference values, then the processcan be stopped as the design goal has been reached.

If, however, the new values for Tangent Vertical Stiffness or SecantVertical Stiffness are lower than the reference values for Tangent andSecant Vertical Stiffness, then E_(membrane)*I_(m) must be increased.Alternatively, even if the new values for Tangent Vertical Stiffness,Secant Vertical Stiffness, Contact Pressure are acceptable, the newvalue for μ_(p/p) may be unacceptable or further reduction may bedesired and, therefore, E_(membrane)*I_(m) must be increased. Toincrease E_(membrane)*I_(m), the value for spacing bias parameter k setforth with equations (7) and (8) above must be decreased incrementally.As the bias parameter k is decreased, the reinforcement layers added tothe shear band that are not located on the neutral fiber will be pushedout toward the outermost and innermost reinforcement layers 130 and 140and this will cause E_(membrane)*I_(m) to increase without impacting thevalue of thickness H_(TARGET), (G_(eff)*A)_(CALC), or(E_(membrane)*A_(m))_(CALC).

Accordingly, for each new value of parameter k selected, another modelof the tire with the shear band construction using the new value forparameter k is constructed and e.g., finite element analysis is used tocompute the four performance characteristics—i.e., the Tangent VerticalStiffness, Secant Vertical Stiffness, Contact Pressure, and μ_(p/p).These new values are again compared to the reference values. If theVertical Stiffness (Tangent, Secant, or both) are less than the valuesof Vertical Stiffness for the reference shear band, then the process ofdecreasing parameter k is continued until the new values exceed or areabout equal to the reference values for Vertical Stiffness. Even if thenew Vertical Stiffness values are acceptable, the process of decreasingparameter k can also be repeated if the value for μ_(p/p) isunacceptable—i.e., too large or higher than the value of μ_(p/p) for thereference shear band 110.

If parameter k reaches zero before the new values of Tangent VerticalStiffness, Secant Vertical Stiffness, and μ_(p/p) reach acceptable ortarget values, then the value of H_(TARGET) must be increased and theprocess must be repeated again starting with one more reinforcementlayer than the reference shear band 110 i.e., N_(REF)+1. Morespecifically, for shear band 110 having NREF=2, the value of H_(TARGET)is increased and a new value for (G_(eff)*A)_(CALC) is calculatedrestarting with a value of N=3 reinforcement layers. This(G_(eff)*A)_(CALC) is then compared to (G_(eff)*A)_(REF), and if(G_(eff)*A)_(CALC) is not greater than or about equal to(G_(eff)*A)_(REF), the process is then repeated by increasing the numberof reinforcement layers N again as previously described.

The method described above was applied to the reference shear band 110having only two reinforcement layers 130 and 140. The results are setforth in Table 3:

TABLE 3 Inputs H N k t W E_(membrane) G_(m) G_(sl) G_(eff) G_(eff) * AI_(m) E_(membrane) * I_(m) A E_(membrane) * A 18 2 1 1.00 230 2000 1000.400 .45 1.862 33,273 66,546,667 460 920,000 15 2 1 1.00 230 2000 1000.400 .46 1,591 22,578 45,156,667 460 920,000 15 3 1 1.00 230 2000 1000.400 .50 1,723 22,598 45,195,000 690 1,380,000 15 4 1 1.00 230 2000 1000.400 .54 1,879 25,121 50,242,222 920 1,840,000 Note: Units are mm anddaN

The first row of data indicates the reference shear band 110 having ashear layer thickness H_(REF) of 18 mm, a width W of 230 mm, and two(N=2) reinforcement layers. The three rows that follow are performedwith the target thickness of H_(TARGET) of 15 mm with the goal ofreducing the thickness of the shear band 110 while maintaining orimproving certain performance characteristics such as vertical stiffnessand μ_(p/p). Although it is perhaps not possible to match theperformance characteristics exactly, as shown in Table 3, a(G_(eff)*A)_(CALC) that exceeded the value (G_(eff)*A)_(REF) for thereference shear band 110 is obtained when four reinforcement layers(N=4) are used. It is again noted that the above-described methodassumes that the construction of tire 100 otherwise remains thesame—i.e., the same materials (e.g., elastomers) are used for the shearlayer 120, the same number of web spokes 150 are used, the same hub isused, etc.

Using the value of four reinforcement layers (N_(TOTAL)=4), tire 100 wasmodeled again and, using finite element analysis, the four performancecharacteristics used in Table 1 (Tangent Vertical Stiffness, SecantVertical Stiffness, Contact Pressure, and μ_(p/p)) were recalculated.The results are set forth in Table 4.

TABLE 4 Vertical Vertical Stiffness Stiffness Contact (Tangent) (Secant)Pressure μ_(p/p) 32.5 daN/mm 40.3 daN/mm 2.31 bar .046 mm

A comparison of Table 4 and Table 1 shows that the thickness of theshear band 110 can be reduced by 3 mm while maintaining its verticalstiffness characteristics. However, Table 4 also provides an unexpectedresult in that μ_(p/p) has actually decreased by reducing the thicknessH of shear band 110 and doubling the number of reinforcement layers.More specifically, the targeted modification of shear band 110 will notonly allow for an increase in the tread portion 105 by 3 mm but willalso result in less radial displacement of the shear band 110 and,therefore, smoother operation of tire 100.

It should be understood that shear layer 120 may be constructed from anymaterial that provides the desired mechanical properties describedherein. While elastomeric materials may be used, the present inventionis not limited to such. For example, materials that may be used forshear layer 120 include those previously described (natural andsynthetic rubbers, polyurethanes, foamed rubbers and polyurethanes,segmented copolyesters, and block co-polymers of nylon) as wellnon-elastomeric materials such as, for example, fiber-reinforcedcomposites or meta-materials. Accordingly, the shear band 110 of thepresent invention is not necessarily limited to a particular materialidentity.

While the present subject matter has been described in detail withrespect to specific exemplary embodiments and methods thereof, it willbe appreciated that those skilled in the art, upon attaining anunderstanding of the foregoing may readily produce alterations to,variations of, and equivalents to such embodiments. Accordingly, thescope of the present disclosure is by way of example rather than by wayof limitation, and the subject disclosure does not preclude inclusion ofsuch modifications, variations and/or additions to the present subjectmatter as would be readily apparent to one of ordinary skill in the artusing the teachings disclosed herein.

What is claimed is:
 1. A method for modifying a shear band of a tire,the tire having a plurality of tension transmitting web spokes extendingtransversely across and radially inward from the shear band toward atire hub, the shear band having a radially innermost reinforcement layerand a radially outermost reinforcement layer extending circumferentiallyaround the shear band, the method comprising the steps of: increasing ormaintaining the vertical stiffness of the tire by adding at least oneadditional reinforcement layer that extends circumferentially around theshear band and is positioned between, but spaced apart from, theradially outermost reinforcement layer and the radially innermostreinforcement layer; decreasing the value of μ_(p/p) for the shear band;and decreasing the thickness, along the radial direction, of the shearband.
 2. A method for modifying a shear band of a tire, the tire havinga plurality of tension transmitting web spokes extending transverselyacross and radially inward from the shear band toward a tire hub, theshear band having a radially innermost reinforcement layer and aradially outermost reinforcement layer extending circumferentiallyaround the shear band, the method comprising the steps of: increasing ormaintaining the vertical stiffness of the tire by adding at least oneadditional reinforcement layer that extends circumferentially around theshear band and is positioned between, but spaced apart from, theradially outermost reinforcement layer and the radially innermostreinforcement layer; and decreasing the value of μ_(p/p) for the shearband, wherein said decreasing further comprises modifying the radialposition of at least one reinforcement layer that is positioned betweenthe radially innermost reinforcement layer and the radially outermostreinforcement layer.
 3. A method for modifying a shear band of a tire,the tire having a plurality of tension transmitting web spokes extendingtransversely across and radially inward from the shear band toward atire hub, the shear band having a radially innermost reinforcement layerand a radially outermost reinforcement layer extending circumferentiallyaround the shear band, the method comprising the steps of: increasing ormaintaining the vertical stiffness of the tire by adding at least oneadditional reinforcement layer that extends circumferentially around theshear band and is positioned between, but spaced apart from, theradially outermost reinforcement layer and the radially innermostreinforcement layer; decreasing the value of μ_(p/p) for the shear band;and maintaining a constant thickness for the shear band during saidsteps of increasing and decreasing.
 4. The method for modifying a shearband of a tire as in claim 3, further comprising the step ofmanufacturing the shear band based on information obtained from saidincreasing and decreasing.
 5. A non-pneumatic tire, comprising: a shearband extending circumferentially around the tire, the shear bandcomprising a shear layer; an inner reinforcement layer positioned alongone side of said shear layer; an outer reinforcement layer positionedalong the other side of said shear layer such that said shear layer ispositioned between said inner and outer reinforcement layers; at leasttwo or more additional reinforcement layers positioned between andspaced apart from each other and from said outer and inner reinforcementlayers such that the shear band has a total of N reinforcement layersand N≧4; and a plurality of tension transmitting web spokes extendingradially inward from the shear band; and wherein the reinforcementlayers comprise essentially inextensible reinforcements.
 6. Thenon-pneumatic tire of claim 5, wherein the inextensible reinforcementsare embedded within an elastomeric coating.
 7. The non-pneumatic tire ofclaim 5, wherein the shear band defines an outer periphery, and furthercomprising a tread portion positioned on the outer periphery of theshear band.
 8. The non-pneumatic tire of claim 5, wherein thereinforcement layers have a tensile stiffness and the shear layer has ashear stiffness, wherein the tensile stiffness is greater than the shearstiffness.
 9. The non-pneumatic tire of claim 5, wherein thereinforcement layers are uniformly spaced from each other.
 10. Anon-pneumatic tire, comprising: a shear band extending circumferentiallyaround the tire, the shear band comprising a shear layer; an innerreinforcement layer positioned along one side of said shear layer; anouter reinforcement layer positioned along the other side of said shearlayer such that said shear layer is positioned between said inner andouter reinforcement layers; at least two or more additionalreinforcement layers positioned between and spaced apart from each otherand from said outer and inner reinforcement layers such that the shearband has a total of N reinforcement layers and N≧4; a plurality oftension transmitting web spokes extending radially inward from the shearband; and a mounting band positioned at a radially inner end of the webspokes, wherein the mounting band is positioned on a wheel hub.